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Nested algorithms for joint DOD and DOA estimation in bistatic MIMO radar

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Abstract

This paper presents two nested algorithms—one based on the Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) algorithm and the other one on the maximum likelihood estimation—for joint direction of departure (DOD) and direction of arrival (DOA) estimation in bistatic multiple-input multiple-output radar. Both of the proposed nested algorithms interweaves signal grouping schemes and DOD/DOA estimation. Thereby, in each stage only DODs or DOAs, but not both, need to be estimated, and thus the complexity called for can be reduced. Also, the signals in each group have close DOAs, yet diverse DODs, and vice versa, so both DODs and DOAs can be precisely estimated even some of them are very close. Additionally, the estimated DODs and DOAs are automatically paired together without extra computations. Also, for the proposed nested-ML, a non-iterative importance sampling-based ML estimator is developed which is ensured to attain global optimum. Simulation results show that the proposed nested-ESPRIT can provide competing performance, yet with much lower complexity compared with the main state-of-the-art works; whereas, nested-ML can reach the Cramer–Rao lower bound with slightly higher complexity.

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Notes

  1. It has been verified in Jin et al. (2009) that even if high Doppler shift exists, the autocorrelation and cross-correlation sidelobes are still low within the zero correlation zone. This implies that Doppler shift has almost no effect on the orthogonality of these waveforms, and thus can be neglected.

  2. In this paper, we use “1-D” to emphasize that we just estimate a single parameter (either DOD or DOA, but not both) and use “2-D” to denote that the DOD and DOA are estimated jointly.

  3. In this paper, we use the fact that one complex multiplication amounts to four real multiplications.

References

  • Bekkerman, I., & Tabrikian, J. (2006). Target detection and localization using MIMO radars and sonars. IEEE Transactions on Signal Processing, 54(10), 3873–3883.

    Article  MATH  Google Scholar 

  • Bencheikh, M. L., & Wang, Y. (2011). Combined esprit-rootmusic for DOA–DOD estimation in polarimetric bistatic MIMO radar. Progress in Electromagnetics Research Letters, 22, 109–117.

    Article  Google Scholar 

  • Bencheikh, M. L., Wang, Y., & He, H. (2010). Polynomial root finding technique for joint DOA DOD estimation in bistatic MIMO radar. Signal Processing, 90(9), 2723–2730.

    Article  MATH  Google Scholar 

  • Bresler, Y., & Macovski, A. (1986). On the number of signals resolvable by a uniform linear array. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(6), 1361–1375.

    Article  MATH  Google Scholar 

  • Chen, J., Gu, H., & Su, W. (2010). A new method for joint DOD and DOA estimation in bistatic MIMO radar. Signal Processing, 90(2), 714–718.

    Article  MATH  Google Scholar 

  • Duofang, C., Baixiao, C., & Guodong, Q. (2008). Angle estimation using ESPRIT in MIMO radar. Electronic Letters, 44(12), 770–771.

    Article  Google Scholar 

  • Fang, W.-H., Lee, Y.-C., & Chen, Y.-T. (2016). Importance sampling-based maximum likelihood estimation for multidimensional harmonic retrieval. IEEE Signal Processing Letters, 23(1), 35–39.

    Article  Google Scholar 

  • Fisher, E., Haimovich, A., Blum, R. S., Cimini, L. J., Jr., Chizhik, D., & Valenzuela, R. A. (2006). Spatial diversity in radars-models and detection performance. IEEE Transactions on Signal Processing, 54(3), 823–838.

  • Golub, G. H., & Van Loan, C. F. (1996). Matrix computations (3rd ed.). Baltimore, MD: Johns Hopkins University Press.

    MATH  Google Scholar 

  • Haardt, M., & Nossek, J. A. (1995). Unitary ESPRIT: How to obtain increased estimation accuracy with a reduced computational burden. IEEE Transactions on Signal Processing, 43(5), 1232–1242.

    Article  Google Scholar 

  • Hamovich, A. H., Blum, R. S., Cimini, L. J, Jr., Chizhik, D., & Valenzuela, R. A. (2008). MIMO radar with widely separated antennas. IEEE Signal Processing Magazine, 25(1), 116–129.

    Article  Google Scholar 

  • Jaffer, A. G. (1988). Maximum likelihood direction finding for stochastic sources: A separable solution. In Proceedings of the IEEE international conference on acoustics, speech, and signal processing (pp. 2893–2896).

  • Jiang, H., Zhang, J.-K., & Wong, K. M. (2015). Joint DOD and DOA estimation for bistatic MIMO radar in unknown correlated noise. IEEE Transactions on Vehicular Technology, 64(11), 5113–5125.

    Article  Google Scholar 

  • Jin, M., Liao, G., & Li, J. (2009). Joint DOD and DOA estimation for bistatic MIMO radar. Signal Processing, 89(2), 244–251.

    Article  MATH  Google Scholar 

  • Kalos, M. H., & Whitlock, P. A. (1986). Monte Carlo methods. New York: Wiley.

    Book  MATH  Google Scholar 

  • Kay, S. (1979). Comments on frequency estimation by linear prediction. IEEE Transactions on Acoustics, Speech, and Signal Processing, 27, 198–199.

    Article  Google Scholar 

  • Lehmann, N. H., Fisher, E., & Haimovich, A. M. (2007). Evaluation of transmit diversity in MIMO-radar direction finding. IEEE Transactions on Signal Processing, 55(5), 2215–2225.

    Article  MathSciNet  Google Scholar 

  • Leon-Garcia, A. (1994). Probability and random processes for electrical engineering (2nd ed.). Boston: Addison-Wesley.

    MATH  Google Scholar 

  • Li, J., Conan, J., & Pierre, S. (2005, December). Joint estimation of channel parameter for MIMO communication systems. In Proceedings of international symposium on wireless communication systems, Siena (pp. 22–26).

  • Lin, J.-H., & Fang, W.-H. (2013). Joint angle and delay estimation in frequency hopping systems. IEEE Transactions on Aerospace and Electronic Systems, 49(2), 1042–1056.

    Article  Google Scholar 

  • Lin, J.-D., Fang, W.-H., Wang, Y.-Y., & Chen, J.-T. (2006). FSF MUSIC for joint DOA and frequency estimation and its performance analysis. IEEE Transactions on Signal Processing, 54(12), 4529–4542.

    Article  MATH  Google Scholar 

  • Li, J., & Stoica, P. (2008). MIMO radar signal processing. Hoboken, NJ: Wiley.

    Book  Google Scholar 

  • Li, J., Stoica, P., Xu, L., & Roberts, W. (2007). On parameter identifiability of MIMO radar. IEEE Signal Processing Letters, 14(12), 968–971.

    Article  Google Scholar 

  • Li, J., & Zhang, X. (2014). Unitary subspace-based method for angle estimation in bistatic MIMO radar. Circuits, Systems, and Signal Processing, 33(2), 501–503.

    Article  MathSciNet  Google Scholar 

  • Mamoudi, A., Bellili, F., Affes, S., & Stephenne, A. (2013). A maximum likelihood time delay estimator in a multipath environment using importance sampling. IEEE Transactions on Signal Processing, 61(1), 182–193.

    Article  MathSciNet  Google Scholar 

  • Pincus, M. (1968). A closed form solution for certain programming problems. Operations Research, 16, 690–694.

    Article  MathSciNet  MATH  Google Scholar 

  • Raleigh, G. G., & Boros, T. (1998). Joint space-time parameter estimation for wireless communication channels. IEEE Transactions on Signal Processing, 46(5), 1333–1343.

    Article  Google Scholar 

  • Roy, R., & Kailath, T. (1989). ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(7), 987–995.

    Article  MATH  Google Scholar 

  • Saha, S. (2001). Optimal estimation of nonlinear and linear parameters in general models. Ph.D. dissertaton. University of Rhode Island.

  • Saha, S., & Kay, S. M. (2002). Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling. IEEE Transactions on Signal Processing, 50(2), 224–230.

    Article  Google Scholar 

  • Tang, B., Tang, J., Zhang, Y., & Zheng, Z. (2013). Maximum likelihood estimation of DOD and DOA for bistatic MIMO radar. Signal Processing, 93(5), 1349–1357.

    Article  Google Scholar 

  • Van Trees, H. L. (2002). Optimum array processing. New York: Wiley-Interscience.

    Book  Google Scholar 

  • Wax, M., & Kailath, T. (1985). Detection of signals by information theoretic criteria. IEEE Transactions on Acoustics, Speech, and Signal Processing, 33(2), 387–392.

    Article  MathSciNet  Google Scholar 

  • Xie, R., Liu, Z., & Wu, J. (2012). Direction finding with automatic pairng for bistatic MIMO radar. Signal Processing, 92(1), 198–203.

    Article  Google Scholar 

  • Yan, H., Li, J., & Liao, G. (2008). Multitarget identification and localization using bistatic MIMO radar systems. EURASIP Journal on Advances in Signal Processing, 2008, 1–8.

  • Zhang, X., Xu, L., Xu, L., & Xu, D. (2010). DOD and DOA estimation in bistatic MIMO radar with reduced-dimension MUSIC. IEEE Communications Letters, 14(12), 1161–1169.

    Article  Google Scholar 

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Acknowledgements

We would like to thank the reviewers for many useful comments and suggestions which have enhanced the quality and readability of this paper.This work was supported by National Ministry of Science and Technology, R.O.C. under contracts MOST 105-2221-E-011-046 and 105-2221-E-011-117.

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Correspondence to Wen-Hsien Fang.

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Fang, WH., Tu, CC. & Chen, YT. Nested algorithms for joint DOD and DOA estimation in bistatic MIMO radar. Multidim Syst Sign Process 29, 783–798 (2018). https://doi.org/10.1007/s11045-017-0511-y

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